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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 4

What type of set is A = {x ∈ Z : x² = 2}?

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Answer and explanation

Correct answer: Empty and finite

There is no integer whose square is 2. The integers nearest to a possible square root are 1 and 2, but 1² = 1 and 2² = 4; in fact, √2 is irrational and is not an integer. Therefore no integer satisfies the defining condition, so A = ∅. The empty set has cardinality zero and is finite.

Tags

setsempty setfinite setintegersirrational numbersThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematics

Frequently asked questions

What is the correct answer to this question?

Empty and finite

Why is this the correct answer?

There is no integer whose square is 2. The integers nearest to a possible square root are 1 and 2, but 1² = 1 and 2² = 4; in fact, √2 is irrational and is not an integer. Therefore no integer satisfies the defining condition, so A = ∅. The empty set has cardinality zero and is finite.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

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